Image stitching for a multi-head printer

ABSTRACT

Techniques are disclosed for stitching images printed by a multi-head printer in a manner that is relatively insensitive to misregistration of the image segments. When a pair of overlapping print heads print a pair of adjacent image segments which meet in a stitching region, printing at each location in the stitching region is accomplished by both print heads with a weighting that depends on the location being printed within the stitching region. In one embodiment, for example, the output of each print head is weighted by a linear function of horizontal pixel position. Techniques are also disclosed for selecting screening patterns for use when stitching is performed with variable-dot printers. Such screening patterns are selected to minimize variations in density that may arise as the result of cross-web and/or down-web misregistration.

BACKGROUND

1. Field of the Invention

The present invention relates to multi-head thermal printers and, inparticular, to thermal printers in which multiple print heads are usedto print a single image in the form of multiple joined segments.

2. Related Art

Various kinds of printers are well-known in the computing and digitalimage arts. Such printers include, for example dot-matrix printers,laser printers, Inkjet printers and thermal printers. The focus of thepresent discussion is on thermal printers, so-named because they usethermal energy (heat) to produce printed output. More specifically,thermal printers typically contain a linear array of heating elements(also referred to herein as “print head elements”) that print on anoutput medium by, for example, transferring pigment from a donor sheetto the output medium or by initiating a color-forming reaction in theoutput medium. The output medium is typically a porous receiverreceptive to the transferred pigment, or a paper coated with thecolor-forming chemistry. Each of the print, head elements, whenactivated, forms color on the medium passing underneath the print headelement, creating a spot having a particular density. Regions withlarger or denser spots are perceived as darker than regions with smalleror less dense spots. Digital images are rendered as two-dimensionalarrays of very small and closely-spaced spots.

A thermal print head element is activated by providing it with energy.Providing energy to the print head element increases the temperature ofthe print head element, causing either the transfer of pigment to theoutput medium or the formation of color in the receiver. The density ofthe output produced by the print head element in this manner is afunction of the amount of energy provided to the print head element. Theamount of energy provided to the print head element may be varied by,for example, varying the amount of power to the print head elementwithin a particular time interval or by providing power to the printhead element for a longer time interval.

A single thermal printer may include multiple thermal print heads, whichmay, for example, be staggered with respect to each other. One exampleof this kind of printer is described in U.S. Pat. No. 4,660,052 to Kaiyaet al., and is described as a heat sensitive recording apparatus withmultiple thermal heads disposed in a staggered arrangement along twoplaten rollers. The apparatus has alternate image segments printed on afirst platen roller by a first set of print heads. The interveningsegments are filled in by a second set of print heads printing on asecond platen roller. The heads are arranged such that the printing ofthe second set of print heads overlaps the printing of the first set ofprint heads, forming “stitching” regions between each pair of adjacentsegments in which the printing may be adjusted to obscure the presenceof a transition from one to the other. In this patent, the method ofjoinery is described as a simple abutment in which a point of transitionis chosen near the center of each stitching region. All pixels to theleft of the transition are printed by the left-hand print head of thepair of overlapping heads, and all pixels to the right of the transitionpoints are printed by the right-hand print head of the pair. This methodof joinery is troublesome, because it lacks robustness towardimperfections in the printer hardware. For example, if the paper motionis not perfectly perpendicular to the print heads, then the paper mayshift slightly to the right or left when traveling from one set of printheads to the other, thereby opening a gap in the stitch or causing anoverlap of image segments. In addition to these mechanicalimperfections, the thermal print head heats up as it prints, and thermalexpansion of the heads can cause a visible overlap of image segments.

U.S. Pat. No. 4,997,410 to Onuki and Denda describes specific means forimplementing an abutted joint as described above by means thatdistribute stitching-region data to the appropriate print heads,depending on whether they are to the right or left of a chosentransition point. This patent describes means for manual readjustment ofthe stitch so as to eliminate any visible gap or overlap, and alsodescribes paeans for automatically compensating for the effects ofthermal expansion of the heads. It would be preferable that no suchmanual adjustments were required for proper operation.

U.S. Pat. No. 5,119,108 to Hatakeyama describes a very similar system,but adds the recommendation that the image segments be overlapped by 2-4pixels, thereby eliminating (for all practical purposes) the possibilityof a gap opening up between the image segments. This, of courseintroduces a 2-4 pixel wide region of higher printed density, which theinventors apparently consider to be unobjectionable due to the verynarrow width of the overlap. This imperfection, however, extends thefull length of the image, and may be visible despite its narrow width.

A solution to this problem is proposed in U.S. Pat. No. 5,450,099 toStephenson and Fiscella. This patent describes a stitch that is moresophisticated than the simple abutted joint. On each line in thestitching region, the pixels to be printed are divided in a randompattern between the two print heads. Each print head printsapproximately one-half of the pixels in the stitch, interleaved so thateach pixel is printed either by one or by the other of the two printheads. On each line, the random division of pixels is changed so thatthere is no recurring pattern from line to line. This avoids correlateddefects that extend the full length of the image, but it does placedemands on the mechanical and thermal tolerances of the printer, as amisregistration of the patterns will result in significant uncontrolledchanges in the printed density of the stitch region. In the case ofmisregistration, approximately 25% of the pixels will be printed by bothprint heads, and 25% of the pixels will not be printed by either printhead. These randomly occurring increases and decreases of density do notcompensate for each other, and an imperfect density is printed.

In view of the drawbacks of these prior-art methods of stitching imagesegments in thermal printers, there is a need for a method of joiningimage segments such that mechanical imperfections in the printerhardware, and thermal expansion of the printer components, will notresult in visible artifacts in the printed image. The consequence ofsuch a method would be an improvement of image quality, and a reductionin the cost of wide-format thermal printers (since a high-precisiontransport mechanism would not be required).

SUMMARY

Techniques are disclosed for stitching images printed by a multi-headprinter in a manner that is relatively insensitive to misregistration ofthe image segments. When a pair of overlapping print heads print a pairof adjacent image segments which meet in a stitching region, printing ateach location in the stitching region is accomplished by both printheads with a weighting that depends on the location being printed withinthe stitching region. In one embodiment, for example, the output of eachprint head is weighted by a linear function of horizontal pixelposition. Techniques are also disclosed for selecting screening patternsfor use when stitching is performed with variable-dot printers. Suchscreening patterns are selected to minimize variations in density thatmay arise as the result of cross-web and/or down-web misregistration.

Other features and advantages of various aspects and embodiments of thepresent invention will become apparent from the following descriptionand from the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A is a diagrammatic representation of an image region in which twosub-regions are printed by a multi-head printer using a prior-artabutment joint and in which the two sub-regions meet exactly at thecenter of a stitching region;

FIG. 1B is a diagrammatic representation of an image region in which twosub-regions are printed by a multi-head printer using a prior-artabutment joint and in which a horizontal misregistration has caused thetwo sub-regions to partially overlap within the stitching region;

FIG. 2 is a graph illustrating the relationship between pixel positionand density in the image region illustrated in FIG. 1A;

FIG. 3 is a graph illustrating the relationship between pixel positionand density in the image region illustrated in FIG. 1B;

FIG. 4 is a graph illustrating weighting functions that are applied tooverlapping print heads according to one embodiment of the presentinvention and the resulting total output density when no misregistrationoccurs;

FIG. 5 is a graph illustrating weighting functions that are applied tooverlapping print heads according to one embodiment of the presentinvention and the resulting total output density when a horizontalmisregistration occurs;

FIGS. 6A-6F are graphs illustrating the application of embodiments ofthe present invention to non-uniform image data;

FIGS. 7A-7B illustrate dot patterns arranged in rectangular grids;

FIG. 7C illustrates the dot patterns of FIGS. 7A-7B overlapped in adot-on-dot arrangement;

FIG. 7D illustrates the dot patterns of FIGS. 7A-7B overlapped in adot-off-dot arrangement;

FIG. 8A illustrates a dot pattern in a staggered arrangement;

FIG. 8B illustrates a dot pattern in a rectangular arrangement

FIG. 8C illustrates the dot patterns of FIGS. 8A-8B overlapping witheach other;

FIG. 9A illustrates four example pixels, each of which includes a singledot in a distinct one of four dot positions;

FIG. 9B illustrates a pattern formed from a repeating pattern of thefour pixels shown in FIG. 9A;

FIGS. 9C-9E illustrate three four-pixel patterns that may be used toperform screening according to embodiments of the present invention;

FIG. 10 illustrates a superimposition of two different four-pixelpatterns;

FIG. 11 illustrates a superimposition of two different three-pixelpatterns with a vertical misregistration; and

FIGS. 12A-12D illustrate four different five-pixel patterns that may beused to perform screening according to various embodiments of thepresent invention,

DETAILED DESCRIPTION

Techniques are disclosed for stitching images printed by a multi-headprinter in a manner that is relatively insensitive to misregistration ofthe image segments. When a pair of overlapping print heads print a pairof adjacent image segments which meet in a stitching region, printing ateach location in the stitching region is accomplished by both printheads with a weighting that depends on the location being printed withinthe stitching region. In one embodiment, for example, the output of eachprint head is weighted by a linear function of horizontal pixelposition. Techniques are also disclosed for selecting screening patternsfor use when stitching is performed with variable-dot printers. Suchscreening patterns are selected to minimize variations in density thatmay arise as the result of cross-web and/or down-web misregistration.

In various embodiments of the present invention, techniques are providedfor use in a printer to stitch images in a manner that is relativelyinsensitive to small and unintended misregistration of the imagesegments. The misregistration may be either “down-web” (i.e., in thedirection of the paper motion), or “cross-web” (i.e., transverse to thepaper motion, and along the print heads).

Referring to FIG. 1A, an image region 100 is shown in diagrammatic formfor purposes of example. The region 100 represents a region of an imageprinted by a multi-head printer using a simple abutment joint, asdescribed above. Region 100 includes two sub-regions 102 a-b. In thepresent example, region 102 a is printed by a first print head 106 a andregion 102 b is printed by a second print head 106 b in a thermalprinter. Print heads 106 a-b are illustrated in block form for ease ofillustration. Paper moves through the printer in the direction indicatedby arrow 108. The patterns illustrated within regions 102 a-b areprovided merely for purposes of example. In actual implementation, theregions 102 a-b may include any image data.

Region 100 also includes a sub-region 104 in which print heads 106 a and106 b overlap. The overlapping region 104 is also referred to herein asa “stitching region” or, more simply, as a “stitch.” For ease ofillustration and explanation, the contents of the regions 102 a-b areillustrated in FIG. 1 using hatch patterns to represent image datahaving constant and equal densities. FIG. 1A illustrates the case inwhich the region 100 is printed with perfect registration, and in whichthe image segments printed by heads 106 a-b therefore meet exactly atthe center line 110 of the stitching region 104 without overlapping. Inthe case of perfect registration, therefore, center line 110 indicatesthe point at which one print head stops printing and the other onebegins.

According to various embodiments of the present inventions, images maybe stitched in a manner that is relatively insensitive to small andunintended misregistration of the image segments (e.g., the regions 102a-b) by abandoning the requirement that each pixel in the stitchingregion 104 be printed by either one of the print heads 106 a-b or by theother. Instead, printing at each location in the stitching region 104 isaccomplished by both print heads 106 a-b, and with a weighting thatdepends on the location within the stitching region 104. On theleft-hand side of the stitching region 104, the media is printedprimarily by the left-hand print head 106 a, and on the right-hand sideof the stitching region 104 it is printed primarily by the right-handprint head 106 b. In this fashion, there is a gradual transition acrossthe stitching region 104 from one of the print heads 106 a-b to theother.

A schematic illustration of the difference between the traditionalabutted joint, and the “graded” joint disclosed herein is made in FIGS.2-3. It is assumed in FIGS. 2-3 that one is attempting to print aconstant density across the stitching region 104. Referring to FIG. 2,for example, a graph 200 is shown which illustrates the relationshipbetween pixel position and density in the case of an abutted joint, inwhich an abrupt transition is made from one of the print heads 106 a-bto the other at the center of the stitching region 104 (as shown in FIG.1A). Curve 204 a illustrates the density printed by the first print head106 a, curve 204 b illustrates the density printed by the second printhead 106 b, and curve 206 illustrates the combined density of curves 204a and 204 b.

In the case of an abutted joint, each of the two overlapping print heads106 a-b prints up to the transition point (at the center of stitchingregion 104 in FIG. 1A), but not beyond. When the paper is movingperfectly from one platen to the other, and the temperature is wellcontrolled, then one may adjust the positions of the print heads 106a-b, and the transition point on each print head, so that the transitionis perfect, resulting in a net density that is perfectly uniform acrossthe stitching region 104. This case is illustrated in FIG. 1A and bycurve 206 in FIG. 2, which is uniform for all positions.

If, however, the print heads 106 a-b expand, or if the paper path isimperfect, the printing from the second print head 106 b mayunintentionally overlap the printing of the first print head 106 a,yielding an overlap region of higher density. Referring to FIG. 1B, forexample, an image region 120 is shown which is similar to the imageregion 100 of FIG. 1A. For example, the region 120 includes sub-regions122 a-b printed by print heads 106 a-b, respectively, on an outputmedium moving in direction 108. The region 120 also includes a stitchingregion 124. For purposes of the present discussion, the contents of thestitching region 124 are illustrated in FIG. 1B to indicate that thepatterns shown in regions 122 a and 122 b are printed at the samedensities within stitching region 124 as those printed outside of thestitching region 124.

As shown in FIG. 1B, sub-regions 122 a-b overlap within a sub-region 112of stitching region 124 as a result of horizontal misregistration. Asindicated in FIG. 1B, as a result of this misregistration, the rightedge 110 a of the sub-region 122 a (printed by print head 106 a) is tothe right of the left edge 110 b of the sub-region 122 b (printed byprint head 106 b), causing the sub-regions 122 a-b to overlap in theregion 112. This overlap causes the overlap region 112 to be of higherdensity than either region 122 a or 122 b.

Referring to FIG. 3, a graph 300 is shown which illustrates therelationship between pixel position and density in the case the region120 shown in FIG. 1B. Curve 304 a illustrates the density printed by thefirst print head 126 a, curve 304 b illustrates the density printed bythe second print head 126 b, and curve 306 illustrates the combineddensity of curves 304 a and 304 b. As illustrated by curve 306, theoverlap between the output printed by the two print heads 126 a-b causesthe total density to spike within the overlap region 112, which is asub-region of the stitching region 124. Alternatively, the paper orprint mechanism may move or distort in such a way that a gap developsbetween the regions 122 a-b, leading to a narrow region of very lowdensity (not shown).

In the following discussion of various embodiments of the presentinvention, reference will be made to output produced by the print heads106 a-b. Although the print heads 106 a-b are illustrated in FIGS. 1A-1Bas producing output using prior art techniques, the same print heads 106a-b may be controlled to produce output according to various embodimentsof the present invention. Furthermore, to the extent that the techniquesdisclosed herein may require modification to the print heads 106 a-b,any description of such techniques should be interpreted to refer toappropriately-modified print heads rather than to the prior art printheads 106 a-b.

Referring to FIG. 4, a graph 400 is shown which illustrates therelationship between pixel position and density in the case of imagesprinted according to various embodiments of the present invention. Curve404 a illustrates the density printed by the first print head 106 a,curve 404 b illustrates the density printed by the second print head 106b, and curve 406 illustrates the combined density of curves 404 a and404 b.

In FIG. 4, the dashed lines indicate a corresponding stitching region408 in the output image. To the left of the stitching region 408 theleft-hand print head 106 a prints the desired density, and within thestitching region 408 the left-hand print head 106 a prints a densitythat is graded from full density to zero density. By the same token, theright-hand print head 106 b prints the desired density to the right ofthe stitching region 408, and within the stitching region 408 theright-hand print head 106 b prints a lower density, graded from right toleft in such a way that the combination of the density printed by theleft and right print heads 106 a-b combines to form the desired density.Although in FIG. 4 the curves 404 a-b are linear and have equal andopposite slopes within the stitching region 408, this is not alimitation of the present invention. Rather, as will be described inmore detail below, other weighting functions may be used to combined theoutput of the print heads 106 a-b within the stitching region 408.

When the paper path is perfect, as in the example shown in FIG. 4, andthe temperature is well controlled, the printing method just describedresults in a density that is uniform across the stitching region 408,just as in the case of the abutted joint. However, in the case of amisregistration, the density change that results from the printingmethod described above with respect to FIG. 4 extends over many pixelsand is of much lower amplitude than in the case of a misregistrationwhen an abutted joint is used.

For example, referring to FIG. 5, a graph 500 is shown which illustratesthe relationship between pixel position and density in the case ofimages printed according to various embodiments of the present inventionwhen there is a misregistration. The meaning of curves 5Q4 a-b and 506are the same as curves 404 a-b and 406 (FIG. 4), respectively.

Assuming for example that the stitching region 508 is 100 pixels wide, amisregistration of 1 pixel results in a density change of only about 1%,peaking in the center of the stitching region 508. In the case that theimage segments move apart from each other, no gap appears between them.Instead, there is a small decrease of density in the misregisteredregion (again about 1% for a 1 pixel misregistration).

This method applies even when the printed material itself is not uniformacross the stitching region. In the more general case, the image data ineach line will vary across the stitch, as illustrated in FIGS. 6A-6F.Referring to FIG. 6A, for example, a graph 600 is shown in which a curve604 represents image data to be printed. As shown in FIG. 6A, curve 604varies in density across stitching region 608.

Referring to FIG. 6B, a graph 610 is shown in which a curve 614represents a linear weighting function to be applied to the output ofthe first print head 106 a. Similarly, referring to FIG. 6C, a graph 620is shown in which a curve 624 represents a linear weighting function tobe applied to the output of the second print head 106 b. The curves 614and 624 show that fraction of the density that will be printed by theprint heads 106 a-b, respectively.

Referring to FIGS. 6D-6E, graphs 630 and 640 illustrate the result ofmultiplying the image data 604 by the weight functions 614 and 624,respectively, and represent the densities to be printed by the printheads 106 a-b, respectively. Referring to FIG. 6F, graph 650 combinesgraphs 600 (FIG. 6A), 630 (FIG. 6D), and 640 (FIG. 6E), and therebyillustrates how the desired total image density 604 is composed from thedensities printed by each of the print heads 106 a-b (illustrated bygraphs 634 and 644, respectively).

In order to implement this method of stitching, it is necessary toconsider the details of the printing method being used. Generallyspeaking, there are two classes of thermal printing methods, referred toas “variable-density” and “variable-dot” printing. In variable-densityprinting, each pixel is filled with a uniform dye density; this uniformdensity changes as heat is applied to the medium. In variable-dotprinting, a dot of maximum density is formed in the pixel; the size ofthe dot increases as heat is applied. The apparent printed density in avariable-dot printer is determined primarily by the fraction of theprinted surface covered by ink. In actuality, printers are not ideal,and may print pixels that are neither uniformly filled with dye norperfect dots of maximum density. However, so-called “dye diffusionthermal transfer” (D2T2) printers are generally considered to bevariable-density in nature, and wax-transfer thermal printers are bestdescribed as variable-dot.

The techniques described above may be applied in a straightforward wayto variable-density printers, although the densities printed by the twoprint heads 106 a-b may not be perfectly additive. Those of ordinaryskill in the art will appreciate that in the event of imperfectadditivity of the two print heads 106 a-b, the resulting printed densitymay be lower or higher than the intended density, and that modificationof the weighting functions for the two print heads 106 a-b may be usedto compensate for the imperfection.

For variable-dot printers, however, there is a further complicationarising from the printing of isolated dots. In particular, invariable-dot printers the printed density in the stitch dependssensitively on whether the dots printed by one print head fall on topof, or in between, the dots printed by another print head. The formercase is referred to as “dot-on-dot” printing, and the latter as“dot-off-dot” printing.

For example, referring to FIGS. 7A-7B, two image segments 702 a-b areshown, each of which is printed in a rectangular grid. Although the dotsin the image segments 702 a-b are shown as having different sizes andpatterns, this is merely to make the two sets of dots distinguishablefrom each other. The dots in image segments 702 a-b are intended torepresent dots having the same size and density. The dot sizes shownrepresent mid-tone densities, for which density shifts frommisregistration are most significant. Dots of larger size may overlapboth when registered and when misregistered, and may even extend intoadjacent pixels. In these cases, the term “dot-off-dot” may be taken tomean the registration giving minimum overlap. Significant overlaps ofthis type tend to subdue density variations and are not illustratedhere. Referring to FIG. 7C, an image 702 c representing a simpledot-on-dot overlap of the images 702 a-b is shown.

A shift of the image segments 702 a-b by one-half pixel with respect toeach other will change the merged image 702 c from a complete dot-on-dotoverlap to a nearly dot-off-dot overlap. This situation is shown byimage segment 702 d in FIG. 7D. Likewise, a down-web misalignment ofdots can also move the dots from complete dot-on-dot alignment to nearlydot-off-dot alignment.

The density change resulting from this change in registration may belarge. If we take the fill-factor of the dots printed by each of theprint heads 106 a-b to be “f”, the density inside the dot to be “Dmax”,and the density outside the dot to be “Dmin”, then the apparent printeddensity on each side of the stitch is shown by Equation 1

D=−log₁₀

(1−f)·10^(−D) ^(min) +f·10^(−D) ^(max)

  Equation 1

It should be appreciated that Equation 1 is approximate and should betaken only as an estimate of the magnitude of the density changes thatwill occur. Equation 1 does not, for example, consider scattering ormultiple reflections in the medium.

For the purposes of estimation, we may take Dmin to be 0, and Dmax to beabout 2, so that this result becomes as shown in Equation 2.

D=−log₁₀

(1−f)+f·10^(−D) ^(max)

≈−log₁₀(1−f)  Equation 2

provided that f is not close to 1. This means that the apparent densitydepends primarily on the fill factor. In a dot-on-dot situation the fillfactor in the stitch region is approximately the same for the overlappedsegments as for the individual unweighted image segments. On the otherhand, when the two segments are dot-off-dot (and provided that the dotsare not large enough to overlap in the dot-off-dot situation) then thefill factor is doubled. In particular, the situation for small values off is indicated by Equation 3:

D≈−log₁₀(e)log_(e)(1−f)≈f·log₁₀(e)  Equation 3

This effect means that the production of a desired density in the stitchas a combination of the weighted density of two overlapping segments isquite difficult for a variable-dot printer, because it requires aknowledge of whether the printing is dot-on-dot or dot-off-dot (orsomewhere between). This, in turn, requires precision control of thepaper transport and of thermal expansion, thereby potentiallycounteracting the benefits of the techniques described above.

A very small change in the printed patterns can change this situationsignificantly. For example, referring to FIGS. 8A-8B, two image segments802 a-b are shown. The second image segment 802 b (FIG. 8B) (like theimage segment 702 b shown in FIG. 7B) is printed in a rectangular grid.The first image segment 802 a (FIG. 8A), however, is printed with itsdots staggered. Referring to FIG. 8C, an image 802 c representing anoverlap of the images 802 a-b is shown.

Staggering the positions of the dark black dots in image 802 a creates asituation in which only half of the dots in the overlap region of theimage 802 c are dot-on-dot. Although it is still true that a cross-webshift of a half-pixel will take us to a nearly dot-off-dot situation, inthe image 802 c there is no positioning that leads to a completelydot-on-dot configuration. In other words, the change in fill factor fromdot-on-dot to dot-off-dot has been reduced by about 2, compared to thesituation illustrated in FIGS. 7A-7D. It is also true that down-webmisregistration in the situation illustrated in FIGS. 8A-8C leads tosmaller variations, since a shift of a half-pixel in that directionbrings us from 50% dot-on-dot overlap back to another 50% dot-on-dotoverlap, and there is no position (for dots of the size illustrated) inthat direction for which the printing is entirely dot-off-dot.

This effect can be further improved by identifying improved dotpatterns. In principle, the dot placement may be varied in both thecross-web and the down-web direction, but conventional print heads haveuniform pixel spacing, and the design of the printer is simplified ifall the print heads have the same pixel spacing. Therefore, thediscussion is limited to the case in which the dot position is onlyvaried in the down-web direction, although this is not a limitation ofthe present invention.

In this case, it is always possible to achieve complete dot-off-dotprinting for small dots by shifting the image segments cross-web so thattheir columns interlace. Departures from this alignment will lead tovarious degrees of dot-on-dot printing. The best patterns are those thatlimit the maximum amount of dot-on-dot overlap, since this will limitthe density variation between the full dot-off-dot printing alignmentand maximum dot-on-dot alignment.

There is also a second constraint, not satisfied by the exampledescribed above with respect to FIGS. 8A-8C. Namely, when the screeningdescribed herein is being used to stitch two image segments, it isdesirable that the two segments have patterns that are similar enoughthat the response curves and thermal corrections will be the same forail image segments. In the example just given with respect to FIGS.8A-8C, a rectangular pattern (FIG. 8B) was combined with a staggeredpattern (FIG. 8A). These two patterns are typically different in bothresponse curve and thermal corrections, and this makes the control ofprinted density and color from one of the segments 802 a-b to the nextquite complicated. Fortunately, in many cases there are distinctpatterns with symmetries that make them equivalent in these aspects.

For ease of explanation, the following discussion is restricted to dotpatterns in which dot location within a pixel is chosen from among a setof N equally spaced down-web locations or “phases,” and the sequence oflocations is a repeating pattern in the lateral direction. This is not,however, a limitation of the present invention.

Consider, for example, the case in which N=4. In this case there arefour equally spaced down-web locations for the dot within the pixel.Referring to FIG. 9A, four example pixels 902 a-d are shown, each ofwhich includes a single dot in a distinct one of the four dot positions(phases). Phases are illustrated in FIG. 9A, and in the remainingfigures, using dashed lines on which dots are centered. The particulardot shapes and sizes used in the drawings are shown merely for purposesof example. More generally, dots may be of any shape and grow outward toany size.

The phases may be numbered from 1 to 4, for example, and may be used inany repeating order. In this illustration, the length of the repeatingorder will be limited to the number of phases, so that each phase willbe represented exactly once in the sequence. The sequences may then belabeled by the sequence of phases. For example, the label 1 3 2 4 refersto the repeating sequence of phases “1 3 2 4 1 3 2 4 1 3 2 4 . . . ”,and will result in lines of pixels forming a pattern 910 shown in FIG.9B. The entire pattern 910 is signified by just four numbers giving theorder of the four phases, in this case 1 3 2 4.

Since there are 4!=24 different ways of arranging four numbers, onemight conclude that there are 24 different patterns available for the4-phase system. However, there are actually only three differentpatterns, because many of the 24 patterns are equivalent. For example,if the pattern above (1 3 2 4) had been described starting in the secondcolumn rather than the first, it would have been called 3 2 4 1,although this clearly describes the same pattern. In other words, anycyclic permutation of the four numbers in a pattern leads to anequivalent pattern.

By the same token, if one describes the same pattern but starting atdifferent phase positions, the result is another set of labels that isdifferent from but equivalent to the original set of labels. Forexample, moving one phase position up-web turns the label 1 3 2 4 into 24 3 1, as may be seen visually from observing FIG. 9B. This is theresult of adding 1 to each number in the original label, and taking theresults modulo 4.

Following these two rules for finding equivalent labels, we find thatthe 16 labels shown in Table 1 all describe exactly the same pattern:

TABLE 1 Cross-Web Shifts Down-Web Shifts 1 3 2 4 3 2 4 1 2 4 1 3 4 1 3 22 4 3 1 4 3 1 2 3 1 2 4 1 2 4 3 3 1 4 2 1 4 2 3 4 2 3 1 2 3 1 4 4 2 1 32 1 3 4 1 3 4 2 3 4 2 1

In other words, of 24 possible labels, 16 are equivalent and describe asingle physical pattern. The remaining 8 fall into two groups of 4, andthen represent diagonal lines of positive and negative slope, asfollows:

-   -   Pattern 1: 1 2 3 4→2 3 4 1→3 4 1 2→4 1 2 3    -   Pattern 2: 4 3 2 1→3 2 1 4→2 1 4 3→1 4 3 2

These two groups have only 4 members rather than 16 because the down-webshifts, in these cases, leads to the same labels as the cross-webshifts.

Therefore, in conclusion, the N=4 case has just three distinct patterns.Referring to FIGS. 9C-9E, examples 920 a-c of each such pattern areshown. Any one of these three patterns 920 a-c may be used on one of theprint heads in a stitch, and another on the other print head. However,the performance will not be equivalent for all pairs. It is desirable tofind two patterns with the property that, no matter what themisregistration, the maximum amount of dot-on-dot overlap is as small aspossible. It is, of course, true that no matter which two patterns arechosen, there is always some registration in which at least one dot ofone pattern is directly on top of one dot of the other one dot perrepeat unit, that is). Therefore, we know that the best we achieve isthat, independent of registration, no more than one dot per repeat unitof the first pattern ever falls directly on top of a dot in the repeatunit of the other.

Consider, for example, the second and third patterns 920 b-c in the caseN=4. These two patterns have the property that although they aredistinct, they have a vertical symmetry that ensures that they willshare a common response curve and thermal control characteristics.However, it is not true that they overlap by only one pixel per unitcell independent of registration. The superposition of the two patterns920 b-c can lead to situations in which two of the four dots per unitcell are registered. Referring to FIG. 10, an example of such asuperimposition 1000 of the two patterns 920 b-c is shown.

The same turns out to be true of any two of the N=4 patterns. Thisleads, then, to the question whether there are any values of N for whichthere are patterns that overlap by at most one pixel per repeat unit.This is a question that may be resolved, for example, by computermodeling. Those of ordinary skill in the art, for example, willunderstand how to implement a software program to generate all possiblepatterns for a particular value of N and to determine which, if any, ofsuch patterns have a worst-case overlap of one dot per repeat unit. Ifany such patterns are found, such patterns may be searched to determinewhether they include any pairs of patterns which are related by asymmetry which signals that they are thermally equivalent (i.e., willhave the same gamma curve and thermal history control). Table 2 listsresults obtained for several values of N using such a computer modelingapproach.

TABLE 2 Number of Number Number of pattern pairs of Number of Distinctwith single dot Phases N Permutations Patterns overlap 3 6 2 1 4 24 3 05 120 8 6 6 720 24 0 7 5040 108 27

Examples will now be described of pattern pairs which satisfy thecriteria just described when the number N of phases is odd. For example,the case of N=3 phases has two patterns, containing the exemplar labels1 2 3 and 3 2 1. When these two patterns are plotted, they appear asshown in the image segment 1100 in FIG. 11. The image segment 1100represents a randomly selected registration.

When these two patterns are misregistered horizontally or vertically,there is no relative position at which more than one dot per unit-cell(the unit-cell being three dots in size) is coincident. This is abenefit to both cross-web and down-web misregistration, as it limits therange of density variations that may occur.

In the case of N=5 there are eight distinct patterns. Four of thesepatterns have the mutual property of not overlapping by more than onedot per unit-cycle. Referring to FIGS. 12A-12D, examples 1200 a-d ofeach of the patterns are shown. From the symmetry of these patterns 1200a-d, we discern that the first and second patterns 1200 a-b will sharethe same response curve and thermal characteristics. The same is true ofthe third and fourth patterns 1200 c-d.

It should be evident that the use of phase patterns to modify thelocation of printed dots on the line will introduce a small amount ofdistortion into the printed image. Those of ordinary skill in the artwill recognize that this distortion may be removed by resampling theimage before printing to arrive at estimates for the image data at thephase-shifted pixel positions at which printing will actually occur.

It is to be understood that although the invention has been describedabove in terms of particular embodiments, the foregoing embodiments areprovided as illustrative only, and do not limit or define the scope ofthe invention. Various other embodiments, including but not limited tothe following, are also within the scope of the claims.

Although the dots in the examples above are circular, this is not alimitation of the present invention. Other dot shapes that may be usedinclude, for example, elliptical dots which are wider than they aretall. When such dots are used there will be less interstitial horizontalspace for dots to move into if horizontal misregistration occurs.

Although the examples provided above are described in relation todensity screening, the same techniques may be applied to color screeningin color images. In this case, each color may be independently stitchedaccording to the techniques just described. The overlaid printing ofthese color separations then leads to a full color image. It isimportant to note, however, that each of the color planes is in itsentirety a variable-dot image, and that its registration with respect toother color planes will affect the color of the printed images.Therefore, it is valuable to use the screening of image segments notonly to improve the quality of the stitches, but also to reduce thevariability of image density and color. Since there is generally noissue of balancing the thermal properties of different color planes,this may be done by using stitches with different numbers of phases onthe different color planes, or by using the same number of phases butdifferent pairs of patterns on each plane. The result will be colorplanes with reduced seam visibility, and with reduced color shift withmisregistration.

Although the examples above involve repeating patterns ofuniformly-sized phases, the present invention is not limited to use inconjunction with such patterns. Rather, embodiments of the presentinvention may, for example, be used with non-repeating patterns and/orwith patterns having phases of non-uniform size.

The techniques described above may be implemented, for example, inhardware, software, firmware, or any combination thereof. The techniquesdescribed above may be implemented in one or more computer programsexecuting on a programmable computer including a processor, a storagemedium readable by the processor (including, for example, volatile andnon-volatile memory and/or storage elements), at least one input device,and at least one output device. Program code may be applied to inputentered using the input device to perform the functions described and togenerate output. The output may be provided to one or more outputdevices.

Each computer program within the scope of the claims below may beimplemented in any programming language, such as assembly language,machine language, a high-level procedural programming language, or anobject-oriented programming language. The programming language may, forexample, be a compiled or interpreted programming language.

Each such computer program may be implemented in a computer programproduct tangibly embodied in a machine-readable storage device forexecution by a computer processor. Method steps of the invention may beperformed by a computer processor executing a program tangibly embodiedon a computer-readable medium to perform functions of the invention byoperating on input and generating output. Suitable processors include,by way of example, both general and special purpose microprocessors.Generally, the processor receives instructions and data from a read-onlymemory and/or a random access memory. Storage devices suitable fortangibly embodying computer program instructions include, for example,all forms of non-volatile memory, such as semiconductor memory devices,including EPROM, EEPROM, and flash memory devices; magnetic disks suchas internal hard disks and removable disks; magneto-optical disks; andCD-ROMs. Any of the foregoing may be supplemented by, or incorporatedin, specially-designed ASICs (application-specific integrated circuits)or Field-Programmable Gate Arrays (FPGAs). A computer can generally alsoreceive programs and data from a storage medium such as an internal diskor a removable disk. These elements will also be found in a conventionaldesktop or workstation computer as well as other computers suitable forexecuting computer programs implementing the methods described herein,which may be used in conjunction with any digital print engine ormarking engine, display monitor, or other raster output device capableof producing color or gray scale pixels on paper, film, display screen,or other output medium.

1-48. (canceled)
 49. A method for use in a multi-head printer to stitcha first and second region of a digital image, the method comprisingsteps of: (A) identifying a stitching region including adjoiningportions of the first and second regions; (B) printing the adjoiningportions of the first and second regions rising both a first and secondprint head in the multi-head printer by performing steps of: (1)weighting the output of the first print head within the stitching regionusing a first weighting function; and (2) weighting the output of thesecond print head within the stitching region using a second weightingfunction; wherein neither the first weighting function nor the secondweighting function is a step function.
 50. The method of claim 49,wherein the first weighting function comprises a linear function havingslope s and wherein the second weighting function comprises a linearfunction having slope −s.
 51. The method of claim 49, wherein themulti-head printer comprises a variable-density printer.
 52. The methodof claim 49, wherein the multi-head printer comprises a variable-dotprinter.
 53. An apparatus for use in a multi-head printer to stitch afirst and second region of a digital mace, the apparatus comprising:means for identifying a stitching region including adjoining portions ofthe first and second regions; means for printing the adjoining portionsof the first and second regions using both a first and second print headin the multi-head printer, the means for printing comprising: means forweighting the output of the first print head within the stitching regionusing a first weighting function; and means for weighting the output ofthe second print head within the stitching region using second weightingfunction; wherein neither the first weighting function nor the secondweighting function is a step function.
 54. The method of claim 53,wherein the first weighting function comprises a linear function havingslope s and wherein the second weighting function comprises a linearfunction having slope −s.
 55. The method of claim 53, wherein themulti-head printer comprises a variable-density printer.
 56. The methodof claim 53, wherein the multi-head printer comprises a variable-dotprinter.